Room-temperature spin injection from a ferromagnetic semiconductor

Abstract

Spin injection using ferromagnetic semiconductors at room temperature is a building block for the realization of spin-functional semiconductor devices. Nevertheless, this has been very challenging due to the lack of reliable room-temperature ferromagnetism in well-known group IV and III-V based semiconductors. Here, we demonstrate room-temperature spin injection by using spin pumping in a BiSb/(Ga,Fe)Sb heterostructure, where (Ga,Fe)Sb is a ferromagnetic semiconductor (FMS) with high Curie temperature (T_C) and BiSb is a topological insulator (TI). Despite the very small magnetization of (Ga,Fe)Sb at room temperature (45 emu/cc), we detected spin injection from (Ga,Fe)Sb by utilizing the large inverse spin Hall effect (ISHE) in BiSb. Our study provides the first demonstration of spin injection at room temperature from a FMS.

Introduction

Room temperature injection and detection of spin-polarized carriers from ferromagnetic semiconductors (FMSs), which possess both the properties of ferromagnets and semiconductors, are crucial for realizing future semiconductor-based spintronics devices^1,2. Indeed, one of the 125 big questions raised about two decades ago was, “Is it possible to create magnetic semiconductors that work at room temperature?”³ So far, all room-temperature spin injection and detection experiments use ferromagnetic metals because of their high Curie temperature (T_C). However, ferromagnetic metals suffer from the “conductivity mismatch” problem when used in heterojunctions with semiconductors, resulting in very low spin injection/detection efficiencies in semiconductor spintronics devices^4,5. Thus, it is crucial to develop ferromagnetic semiconductors with high T_C and room-temperature spin injection capability. Meanwhile, successful spin injection has been reported only in prototypical Mn-doped III-V FMS (Ga,Mn)As at very low temperature < 120 K^6–8. This is because these Mn-doped FMSs show ferromagnetic order only at low temperature (the maximum Curie temperature T_C is 200 K in (Ga,Mn)As)⁹. Recently, Fe-doped III-V FMSs, such as (In,Fe)As, (Ga,Fe)Sb, and (In,Fe)Sb, are shown to be promising because of their high T_C (> 300 K)^10–17. The origin of ferromagnetism as well as the electronic structures and magnetic properties of Fe-doped FMSs have also been studied by first-principles calculations^18,19, which suggest that the ferromagnetic interaction between Fe atoms occurs at the second nearest-neighbor and third nearest-neighbor in the semiconductor hosts. It is also shown that high T_C in Fe-doped FMSs may come from high impurity concentration and is not due to the carrier-induced mechanism because Fe³⁺ does not introduce carriers²⁰. Furthermore, T_C over 1000 K for Fe-doped FMSs is predicted, based on n- or p-type Fermi level shift²¹. Thus, Fe-doped FMSs are very promising for future applications because high Curie temperature (T_C > 500 K) is necessary for practical applications²². Very recently, a giant magnetoresistance over 500% was observed in n-type (In,Fe)As/p-type (Ga,Fe)Sb spin diodes at low temperatures²³. Despite all of these intensive efforts, room-temperature spin injection from Fe-doped FMSs has not yet been demonstrated.

Recently, we show macroscopic ferromagnetism in (Ga,Fe)Sb by observing clear ferromagnetic resonance (FMR) at room temperature^12,13. So far, spin pumping^24,25, electrical spin injection^26,27, spin Seebeck effect²⁸, and other optical methods²⁹ have been used to study the spin injection from a ferromagnetic (FM) layer into a non-magnetic (NM) layer. Among those methods, spin pumping, which employs FMR, is one of the most efficient methods, because a pure spin current can be transported through a FM/NM interface even under a conductivity mismatch condition³⁰. The injected spin current is detected by the inverse spin Hall effect (ISHE) in the NM layer, which converts the spin current to a charge current via spin–orbit interaction (SOI)³¹. The efficiency of this spin-to-charge conversion is characterized by the inverse spin Hall angle (ISHA). However, because the ISHE output voltage is proportional to the magnetization of the FM layer, which is only 45 emu/cc for (Ga,Fe)Sb at room temperature, one needs to use a spin Hall material with a large spin Hall effect as the spin detector. From this viewpoint, topological insulators can be utilized to detect spin injection from the (Ga,Fe)Sb^32,33. Recently, it was found that Bi_1-xSb_x (0.07 ≤ x ≤ 0.22) is a three-dimensional topological insulator (TI) with strong SOI and large spin Hall angle (SHA) > 1³⁴. This large SHA was also observed in non-epitaxial BiSb layers deposited by magnetron sputtering^35–39, which means that poly-crystalline BiSb can also be used for spin detection by using its large SHA. Non-trivial topologically protected surface states of BiSb have been confirmed by angle-resolved photoemission spectroscopy (ARPES)^40–42, quantum oscillations^43,44, resistivity-temperature characteristics^45,46, and very recently, scanning tunneling microscopy (STM) measurements⁴⁷.

In this work, we prepare a BiSb/(Ga,Fe)Sb heterostructure, where we use (Ga,Fe)Sb (T_C > 300 K) as a FMS layer and BiSb as the NM layer, and demonstrate spin injection by spin pumping and spin detection by ISHE at room temperature. Furthermore, by carefully analyzing the voltage signals at various magnetic field directions, temperatures, and microwave powers, we distinguish the intrinsic ISHE signals from parasitic galvanomagnetic contributions, such as anomalous Hall effect (AHE) and planar Hall effect (PHE)^8,48,49. Our study provides an important step towards realization of room-temperature semiconductor spintronics devices, such as spin diodes and spin transistors.

Results

Sample growth and experimental procedure

Figure 1a (top panel) shows the schematic structure of our sample. In the BiSb/(Ga_0.75,Fe_0.25)Sb heterostructure, (Ga,Fe)Sb layer was first grown by molecular beam epitaxy (MBE) followed by BiSb growth using sputtering (see “Methods”). The growth process was monitored in situ by reflection high-energy electron diffraction (RHEED). Figure 1b–d (top panel) show RHEED patterns observed along the $[\overline{1}\text{1}0]$ axis of the sample. During the MBE growth, the (Ga,Fe)Sb thin film showed bright and streaky RHEED [Fig. 1b (top panel)], thereby indicating good two-dimensional growth of a zinc-blende crystal structure. After etching the GaSb cap layer, we observed spotty RHEED, indicating that the (Ga,Fe)Sb surface is exposed [Fig. 1c (top panel)]. Finally, we observed a ring RHEED pattern after depositing BiSb [Fig. 1d (top panel)], indicating poly-crystalline BiSb in our sample. In this way, we deposited a poly-crystalline BiSb film on top of the epitaxial (Ga,Fe)Sb thin film. We characterized the magnetic properties of the BiSb (7 nm)/(Ga,Fe)Sb (50 nm) heterostructure (sample A) and a reference (Ga,Fe)Sb (50 nm) thin film (sample B) using magnetic circular dichroism (MCD) spectroscopy and superconducting quantum interference device (SQUID) magnetometry (see Sections 1 and 2 in the Supplementary Information (S.I.) for detailed characterizations). From the MCD and SQUID characterizations, we confirmed the intrinsic ferromagnetism of (Ga,Fe)Sb in both samples A and B, and that (Ga,Fe)Sb is not affected by the etching of the GaSb cap layer and the BiSb overgrowth. Also, we note that 50 nm-thick (Ga_0.75,Fe_0.25)Sb has in-plane magnetic anisotropy at room temperature but changes to perpendicular magnetic anisotropy at low temperatures⁵⁰. These results are further supported by magnetic-field angle dependence of the FMR spectra of (Ga,Fe)Sb in samples A and B, which indicates that there is almost no difference in magnetic anisotropy and the FMR occurs at the same resonance fields in both samples (see Section 3 in S.I. for more details).

Figure 1.

(a) Schematic illustration of the (001)-oriented sample structure composed of BiSb (7 nm)/(Ga,Fe)Sb (50 nm)/AlSb (100 nm)/AlAs (10 nm)/GaAs (50 nm) grown on a semi-insulating (SI) GaAs (001) substrate. (b–d) In-situ reflection high energy electron diffraction (RHEED) patterns observed along the $[\overline{1}\text{1}0]$ axis with a streaky RHEED pattern during the MBE growth of (Ga,Fe)Sb (b), a spotty RHEED pattern of the interface after anti-sputtering (c), and a ring RHEED pattern of BiSb during sputtering (d). The black dotted line in (c) corresponds to the interface between BiSb and (Ga,Fe)Sb layer. (e) Sample alignment and coordinate system used in the spin pumping measurement. A microwave magnetic field μ₀h was applied along the [110] axis of the sample. θ_H is the angle of the magnetic field H with respect to the [001] axis, respectively, where H is in the (110) plane. (f) Ferromagnetic resonance (FMR) spectra and (g) corresponding electromotive force (EMF) voltage peaks of the BiSb/(Ga,Fe)Sb heterostructure (sample A) measured at various magnetic field H directions (θ_H = −90° to 90°) at 300 K.

For spin pumping measurements, we used an electron spin resonance spectrometer whose cavity resonates in the transverse electric TE₀₁₁ mode at a microwave frequency of 9.14 GHz. Figure 1e (top panel) shows the BiSb/(Ga,Fe)Sb bilayer structure and coordinate axes used in our spin pumping experiment. For electrical measurements, we have connected the two gold wires at both edges of the sample with a distance of l = 2 mm apart as shown in Fig. 1e (top panel). For the measurements, a static magnetic field μ₀H is applied along the $[1\overline{\text{1}}0]$ direction in the film plane (i.e. θ_H = 90°), which corresponds to the easy magnetization axis of (Ga,Fe)Sb. Here, θ_H is the out-of-plane angle between H and the [001] axis. A microwave magnetic field μ₀h was applied along the [110] axis. The detailed measurement procedure is described in S.I.

Room-temperature spin pumping and spin-to-charge conversion

Figure 1f (bottom panel) shows the FMR spectra at various θ_H measured at a microwave power of 200 mW. The resonance field μ₀H_R of the FMR spectra changes from 290 to 336 mT when θ_H is changed from ± 90° (H // $[1\overline{\text{1}}0]$ and [$\overline{\text{1}}10$]) to 0° (H // [001]). This indicates that the 50 nm-thick (Ga_0.75,Fe_0.25)Sb film in this work has the in-plane magnetic anisotropy with an easy magnetization axis along the $[1\overline{\text{1}}0]$ axis at 300 K. Figure 1g (bottom panel) shows the electromotive force (EMF) signal V (offset voltage V_offset is subtracted) at various θ_H. As shown in Fig. 1g (bottom panel), the V–μ₀H curves exhibit voltage extrema corresponding to the resonance fields (μ₀H_R) in the FMR spectra, which indicates that the observed voltage signals were generated by FMR. Also, the θ_H-dependence of EMF is consistent with the formula EMF ∝ j_S × σ, where j_S and σ are the spin current and spin polarization vector of the spin current, respectively^51,52. When θ_H is changed from 90° to –90°, the voltage signal changes its sign from positive to negative, but its magnitude is the same, which cannot be explained by the Seebeck effect. The maximum EMF signal is obtained at θ_H = 90° and –90°, where j_S is perpendicular to the σ. On the other hand, the EMF signal disappears at θ_H = 0°, when j_S is parallel to σ. This indicates that the observed EMF signal is consistent with the well-established model of spin injection by spin pumping and spin-to-charge conversion by ISHE.

Next, we investigated EMF vs. magnetic field (μ₀H) at various microwave power magnitudes to further confirm the ISHE in our sample. Figure 2a,b show the microwave power dependence of EMF for sample A at 300 K for θ_H = 90° (H // [$1\overline{\text{1}}0$]) and –90° (H // [$\overline{\text{1}}10$]), respectively. We note that in both directions, the EMF is proportional to the applied microwave power, which further discards the contribution of the Seebeck effect⁵³. Next, for qualitative analysis, we decomposed the obtained EMF–μ₀H curves into a symmetric (Lorentzian) voltage component $V_{\text{sym}}^{\ast }$ and an asymmetric (dispersive) voltage component $V_{\text{asym}}^{\ast }$, using the following fitting expression:

$$\begin{array}{cc}\hfill \text{EMF (}V-V_{\text{offset}})& =V_{\text{sym}}^{\ast }+V_{\text{asym}}^{\ast },\hfill \\ \hfill & =V_{\text{sym}}\frac{{\left({\mu }_0,\mathrm{\Delta },H\right)}^2}{{\left({\mu }_0,H,,-,,{{\mu }_{0}H}_{\text{R}}\right)}^2+{\left({\mu }_0,\mathrm{\Delta },H\right)}^2}+V_{\text{asym}}\frac{-2{\mu }_0\mathrm{\Delta }H({\mu }_{0}H-{{\mu }_{0}H}_{\text{R}})}{{\left({\mu }_0,H,,-,{{\mu }_{0}H}_{\text{R}}\right)}^2+{\left({\mu }_0,\mathrm{\Delta },H\right)}^2},\hfill \end{array}$$ 1

where μ₀ΔH is the half-width at half maximum of the FMR linewidth and μ₀H_R is the resonance field. Here, V_sym is the magnitude of symmetric (Lorentzian) voltage component and V_asym is the magnitude of an asymmetric (dispersive) voltage component. According to a previous work on spin pumping using (Ga,Mn)As, V_sym includes contributions from the ISHE and PHE, while V_asym originates from the AHE⁸. As shown in Fig. 2a,b, the experimental data (solid curves) is well reproduced by the fitting function (black dotted curves) of Eq. (1). From Fig. 2c, the estimated V_sym and V_asym components are directly proportional to the applied microwave power, which is an important identity of ISHE. This is also evidenced by the θ_H dependence of the EMF [Fig. 1g (bottom panel)], where we observed nearly similar voltage extrema ~ 6 μV when θ_H = 90° (H // [1$\overline{\text{1}}$0]) and −90°(H // [$\overline{\text{1}}$10]).

Figure 2.

(a) and (b) Magnetic field μ₀H dependences of the voltage signal V (offset voltage V_offset is subtracted) in the BiSb/(Ga,Fe)Sb heterostructure (sample A) measured at 300 K at various microwave powers, ranging from 10 to 200 mW, for θ_H = 90° and –90°, respectively. The black dotted curves represent fitting which includes a summation of the symmetric and antisymmetric voltage components. (c) Microwave power dependence of the symmetric voltage component magnitude V_sym and antisymmetric voltage component magnitude V_asym at θ_H = 90° and –90°. The errors bars in (c) are standard deviations obtained from the fitting of the EMF peaks.

Next, in order to distinguish the contribution of spin-pumping to V_sym from the parasitic contribution of the PHE in sample A [BiSb/(Ga,Fe)Sb], we performed the FMR measurements on the reference sample B [(Ga,Fe)Sb without BiSb]. In Fig. 3a–c, we compare the EMF signals of sample A and sample B at various θ_H. While we notice both the strong symmetric and asymmetric components in sample A, the symmetric component is absent in sample B. This result suggests that the contribution of the PHE to V_sym in (Ga,Fe)Sb is negligible. This also negates the contribution of anomalous Nernst effect (ANE) in (Ga,Fe)Sb which also has the symmetric component V_sym. We then use Eq. (1) to fit to the voltage signals and estimate the magnitude of the voltage components V_sym and V_asym for sample A and $V_{\text{sym}}^{\text{ref}}$ and $V_{\text{asym}}^{\text{ref}}$ for reference sample B. Figure 3d shows the estimated voltage components as a function of θ_H. We see that $V_{\text{sym}}^{\text{ref}}$<< $V_{\text{asym}}^{\text{ref}}$ (~ 100 times different) for sample B, which means that the voltage contribution from PHE of (Ga,Fe)Sb is negligible at 300 K. Meanwhile, the parasitic contribution from AHE of (Ga,Fe)Sb at 300 K to the asymmetric voltage component exists in both samples. However, in the case of sample A, V_sym > V_asym, which means that ISHE is stronger and dominant over AHE.

Figure 3.

(a)–(c) Voltage signals V–V_offset for the BiSb/(Ga,Fe)Sb heterostructure (sample A, red big circles) and reference (Ga,Fe)Sb sample (sample B, green small circles) observed for various magnetic field H directions (θ_H) at 300 K, where H is in the (110) plane. The microwave power is 200 mW. Blanked circles are experimental data, and a black color dotted line is a fitting curve. Symmetric and antisymmetric component curves, obtained from the fitting, are also shown by small solid circles and squares, respectively. (d) The derived symmetric voltage component magnitude (V_sym) and antisymmetric voltage component magnitude (V_asym) of sample A (red solid symbols) and sample B (green blank symbols) at 300 K. The circles and squares represent V_sym and V_asym, respectively. The errors bars in (d) are standard deviations obtained from the fitting of the EMF peaks.

Temperature dependence of the spin injection by spin-pumping

Next, we investigated the temperature dependence of the spin injection by spin pumping from (Ga,Fe)Sb to BiSb. Figure 4a shows the temperature dependence of the resistivity of samples A and B. We note that sample A (with the BiSb layer, red circles) shows larger conductivity than sample B (without BiSb, black circles) at all temperatures, which reflects the much higher electrical conductivity of the BiSb layer³⁷. The estimated electrical conductivities (σ_GaFeSb, σ_BiSb) of (Ga,Fe)Sb and BiSb at 300 K are shown in Table 1. Because σ_BiSb (1.8 × 10⁵ Ω⁻¹ m⁻¹) >  > σ_GaFeSb (1.4 × 10³ Ω⁻¹ m⁻¹), the charge current mostly flows in the BiSb layer. In previous studies on BiSb thin films^35,45,46, contribution of the topological surface states (SSs) to the total conductivity of the BiSb layer was estimated by using the parallel conduction model of the surface states and the bulk states. There, it was reported that a 10-nm-thick BiSb layer has a large bandgap of ~ 200 meV due to the quantum size effect, and that the SSs account for ~ 95% of the total current in BiSb even at room temperature. We used a similar parallel conduction model for our 7 nm-thick BiSb thin film and found that ~ 97% of the current flows in the SSs of BiSb at room temperature (see Sections 5–7 in S.I. for more details). This is also consistent with the recent observation using STM in 5.5 nm-thick BiSb thin films, where the band gap of BiSb is found to be further increased to 490 meV due to the strong quantum confinement, and that the Fermi level is in the band gap, so that most of the current flows in the SSs of BiSb⁴⁷. We will use this information later for the estimation of the ISHA of BiSb.

Figure 4.

(a) Temperature dependence of the resistivity of the BiSb (7 nm)/(Ga,Fe)Sb (50 nm) heterostructure (sample A, red open circles) and the 50 nm-thick (Ga,Fe)Sb reference (sample B, black open circles). (b) Perpendicular magnetic field μ₀H dependence of the anomalous Hall resistance (R_AHE) of sample B measured at various temperatures. (c) Saturation values (${\mathit{\text{R}}}_{\text{AHE}}^{\text{0}}$) of R_AHE as a function of temperature in sample B. (d) In-plane magnetic field direction (φ_H) dependence of the planar Hall resistance (R_PHE) of sample B with the applied magnetic field of 50 mT, 80 mT, and 100 mT measured at 300 K. φ_H is the angle of the in-plane magnetic field with respect to the [$1\overline{\text{1}}0$] axis. (e) μ₀H dependences of the voltage signal V (offset voltage V_offset is subtracted) of sample A measured with 200 mW at various temperatures, ranging from 300 to 10 K, for θ_H = 90°. The black dotted curves represent fittings which were used to derive the magnitude of the symmetric voltage (V_sym) and antisymmetric voltage (V_asym) components. (f) V_sym and V_asym of sample A as a function of temperature. Red solid circles and black solid squares represent V_sym and V_asym, respectively. The errors bars are standard deviations obtained from the fitting of the EMF peaks.

Table 1.

Parameters used for the ISHA estimation.

l (mm)	dGaFeSb (nm)	dBiSb (nm)	${\sigma }_{\text{GaFeSb}}$ (Ω−1 m−1)	${\sigma }_{\text{BiSb}}$ (Ω−1 m−1)	VISHE (μV)
2	50	7	1.4 × 103	1.8 × 105	4.4 ± 0.3

l is the distance between the gold wire contacts, d_GaFeSb and d_BiSb are the thickness of the (Ga,Fe)Sb layer and the BiSb layer, respectively. σ_GaFeSb and σ_BiSb are the electrical conductivities of the (Ga,Fe)Sb layer and the BiSb layer estimated from transport measurements, respectively. V_ISHE (= V_sym) is the ISHE voltage signal estimated by the maximum peak height of the symmetric component of the voltage signal after removing the offset value. All parameters are estimated at 300 K, at a microwave power of 200 mW with a magnetic field H direction of θ_H = 90° (H // $[1\overline{\text{1}}0]$).

We then evaluated the temperature dependence of AHE in reference sample B [(Ga,Fe)Sb without BiSb]. For this purpose, we prepared a Hall bar of 200 μm (length) × 50 μm (width) and measured the temperature dependence of AHE with H // [001]. Figure 4b shows the anomalous Hall resistance (R_AHE) as a function of temperature, which increases with decreasing temperature. We know that the saturation values of R_AHE, $R_{\text{AHE}}^0$, reflects the AHE from the (Ga,Fe)Sb film; however, due to the presence of the ordinary Hall effect (OHE) along with the AHE, it is difficult to saturate R_AHE, especially at high temperatures. Thus, we use R_AHE values at 1 T as $R_{\text{AHE}}^0$ which is closer to the saturation values of R_AHE. Figure 4c shows $R_{\text{AHE}}^0$ as a function of temperature in sample B, where we see a clear increase in $R_{\text{AHE}}^0$ with decreasing temperature. We also measured the planar Hall resistance (R_PHE) as a function of in-plane H angle φ_H (where φ_H is the angle between H and the [1$\overline{\text{1}}$0] axis), at a constant μ₀H of 50 mT, 80 mT, and 100 mT at 300 K [Fig. 4d]. We note that in comparison with $R_{\text{AHE}}^0$ (= ~ 9 Ω), R_PHE (= ~ 0.6 Ω) is much smaller at 300 K. Furthermore, although R_PHE would follow cos(2φ_H) dependence, R_PHE is actually dominated by the cos(φ_H) component (see Fig. 4d). This cos(φ_H) component is due to a small misalignment of the magnetic field from the xy plane, leading to the AHE contribution, while the PHE contribution of $R_{\text{PHE}}^0$ cos(2φ_H) is negligible in Fig. 4d, where $R_{\text{PHE}}^0$ is the magnitude of R_PHE. Therefore, we conclude $R_{\text{PHE}}^0$ << $R_{\text{AHE}}^0$ at room temperature. This result is consistent with the absence of the V_sym component in sample B observed in Fig. 3d.

Next, we measured the temperature dependence of the EMF at θ_H = 90° in sample A, as shown in Fig. 4e. We found that the EMF peak position i.e. resonance field (μ₀H_R) changes from 290 to 270 mT when temperature decreases from 300 to 10 K. This change is likely because μ₀H_R depends on the magnetic anisotropy and the magnetization, both of which have temperature dependency. However, the magnitude and shape of the EMF signals depend on temperature. For example, the EMF peak at 10 K is significantly broader than that at 300 K. To understand this behavior, we fit Eq. (1) to the experimental data to estimate V_sym and V_asym at each temperature. Figure 4f shows the temperature dependence of V_sym and V_asym. At low temperatures, we see clear enhancement of parasitic component V_asym by a factor of 3 at 10 K as compared with that at 300 K, which is consistent with the temperature dependence of R_AHE shown in the Fig. 4c. Meanwhile, V_sym shows close values (4.1 ± 0.2–5.1 ± 0.2 µV) at all temperatures, suggesting that the spin injection by spin pumping has small temperature dependence.

Estimation of spin-to-charge conversion efficiency

In this section, we estimate the spin-to-charge conversion efficiency of BiSb, and discuss why BiSb is important to detect spin injection by spin pumping from (Ga,Fe)Sb. We first estimated the spin current density $j_{\text{S}}^{\text{BiSb/GaFeSb}}$ in sample A [BiSb/(Ga,Fe)Sb] by using the following equation²⁵:

$$j_{\text{S}}^{\text{BiSb/GaFeSb}}=\frac{g_{\text{r}}^{\uparrow \downarrow }{\gamma }^2{\left({\mu }_0,\mathit{\text{h}}\right)}^2ħ\left(4,\pi ,{\mu }_0,M_{\text{S}},\gamma ,+,\sqrt{{\left(4,\pi ,{\mu }_0,M_{\text{S}},\gamma \right)}^2+4{\omega }^2}\right)}{8\pi {\alpha }^2\left[{\left({4\pi {\mu }_{0}M}_{\text{S}},\gamma \right)}^2,,+,4,{\omega }^2\right]},$$ 2

Here, γ = gμ_B/$ħ$ is the gyromagnetic ratio, where g, μ_B, and $ħ$ are the g factor, Bohr magneton, and Dirac’s constant, respectively, and α = $\sqrt{3}\gamma {\mathrm{\Delta }H}_{\text{BiSb/GaFeSb}}/2\omega$ is the damping constant, and μ₀ΔH_BiSb/GaFeSb (= 35 ± 0.5 mT) is the FMR spectral linewidth of sample A when H // [$1\overline{\text{1}}0$]. Also, μ₀h, μ₀M_S, and $g_{\text{r}}^{\uparrow \downarrow }$ are the microwave magnetic field, saturation magnetization, and real part of the spin mixing conductance, respectively. The real part of the spin mixing conductance is obtained by

$$g_{\text{r}}^{\uparrow \downarrow }=\frac{2\sqrt{3}\pi {\mu }_0{M}_{\text{S}}\gamma d_{\text{GaFeSb}}}{g{\mu }_{\text{B}}\omega }\left(\mathrm{\Delta },H_{\text{BiSb/GaFeSb}},-\mathrm{\Delta },H_{\text{GaFeSb}}\right),$$ 3

where μ₀ΔH_GaFeSb (= 32 ± 0.5 mT) is the FMR spectral linewidth of sample B when H // [$1\overline{\text{1}}0$] and d_GaFeSb is the thickness of the (Ga,Fe)Sb film. Using Eqs. (2), (3), and the parameters shown in Table 2, we estimated the value of $g_{\text{r}}^{\uparrow \downarrow }$ and spin current density $j_{\text{S}}^{\text{BiSb/GaFeSb}}$ at the BiSb/(Ga,Fe)Sb interface at 300 K. The values of $g_{\text{r}}^{\uparrow \downarrow }$ and $j_{\text{S}}^{\text{BiSb/GaFeSb}}$ are estimated to be 1.20 × 10¹⁹ m⁻² and (5.35 ± 0.21) × 10^–12 J m⁻², respectively.

Table 2.

Parameters obtained by fitting our model to the experimental FMR spectra.

μ0ΔHBiSb/GaFeSb (mT)	μ0ΔHGaFeSb (mT)	μ0h (mT)	μ0HR (mT)	μ0MS (mT)	γ × 1011 (T−1 s−1)	ω × 1010 (s−1)	g factor
35 ± 0.5	32 ± 0.5	0.055	290	56 ± 2	1.84 ± 0.02	5.74	2.09 ± 0.03

ΔH_BiSb/GaFeSb and ΔH_GaFeSb are the FMR spectral linewidths for sample A and sample B when magnetic field H // $[1\overline{\text{1}}0]$, respectively; μ₀h, μ₀H_R, ω, and g are the microwave magnetic field, resonance field, angular microwave frequency, and g factor, respectively. γ = gμ_B/ℏ is the gyromagnetic ratio and μ₀M_S is the saturation magnetization measured by SQUID.

Finally, we estimated ISHA by using the well-known expression²⁵:

$$V_{\text{ISHE}}=\frac{l{\theta }_{\text{ISHE}}{\lambda }_{\text{BiSbtanh}}\left(d_{\text{BiSb}},/,2,{\lambda }_{\text{BiSb}}\right)}{{\sigma }_{\text{GaFeSb}}{d}_{\text{GaFeSb}}+{\sigma }_{\text{BiSb}}{d}_{\text{BiSb}}}\left(\frac{2\text{e}}{ħ}\right)j_{\text{S}}^{\text{BiSb/GaFeSb}},$$ 4

where, σ_GaFeSb, σ_BiSb, d_GaFeSb, d_BiSb are the electrical conductivities and thicknesses of the (Ga,Fe)Sb and BiSb layers, respectively; l is the length between the electrodes, e is the electron charge, $ħ$ is the Dirac constant, and θ_ISHE is the inverse spin Hall angle. The estimated values of these parameters are shown in Table 1. As we discussed above, conduction of the charge current in BiSb occurs only in the SSs of the BiSb. Thereby, we modify Eq. (4) by replacing d_BiSb with d_S and λ_BiSb with λ_S in the numerator part, where d_S and λ_S are the thickness and spin diffusion length of the surface states in the BiSb layer. It is reported that the surface state thickness and spin diffusion length of Bi is d_S = 2.0 ± 0.2 nm and λ_S = 2.4 ± 0.3 nm⁵⁴. Because BiSb in this work is a topological insulator with a band gap significantly larger than that of Bi, the surface state thickness is expected to be thinner than that of Bi. Therefore, we assume that d_S ~ λ_S = 1.0–1.2 nm in Bi_0.85Sb_0.15⁴¹. The modified expression for ISHA estimation based on the dominant surface conduction is given by

$$V_{\text{ISHE}}=\frac{l{\theta }_{\text{ISHE}}{d}_{\text{Stanh}}\left(1,/,2\right)}{{\sigma }_{\text{BiSb}}{d}_{\text{BiSb}}}\left(\frac{2\text{e}}{ħ}\right)j_{\text{S}}^{\text{BiSb/GaFeSb}},$$ 5

Using the parameters in Table 1 and Eq. (5), we estimated ISHA ${\theta }_{\text{ISHE}}$ ~ 2.1–2.6. This ${\theta }_{\text{ISHE}}$ is close to the SHA value θ_SHE ~ 3.2 reported for non-epitaxial BiSb grown by MBE³⁵ and 2.0–2.4 for sputtered BiSb^36,37. As shown in Table 3, the spin-to-charge conversion efficiency at 300 K of BiSb is much larger than those reported in literature. Nevertheless, in the present study, we deposited poly-crystalline BiSb by sputtering on the etched surface of MBE-grown (Ga,Fe)Sb, which may have led to lower ISHA. Thus, an even higher ISHA value may be obtained by growing both BiSb and (Ga,Fe)Sb epitaxially. This large spin-to-charge conversion efficiency of BiSb is the key to detect spin injection by spin-pumping from (Ga,Fe)Sb with the tiny M_S ~ 45 emu/cc at room temperature, which is 40 times smaller than that of Fe (1800 emu/cc).

Table 3.

Comparison of the spin-to-charge conversion efficiency between our sample with other heterostructures.

Sample structure	T (K)	${\theta }_{\text{ISHE}}$ at 300 K	Reference
Ni81Fe19/p-Si	300	0.0001	Ref.55
Co/Pt and Co/Cu/Pt	300	0.056	Ref.56
Au/Fe/Ag/α-Sn	300	0.62	Ref.57
SiO2/NiFe/Bi2Se3	15–300	0.0093	Ref.58
Ni81Fe19/Sn-Bi2Te2Se	15–300	0.0001	Ref.53
(Ga,Fe)Sb/BiSb	300	2.1–2.6	This work

T is a temperature at which ISHE voltage signals were measured and θ_ISHE is the spin-to-charge conversion efficiency.

Conclusion

We have demonstrated spin injection by spin pumping and detection by ISHE in a BiSb/(Ga,Fe)Sb heterostructure at room temperature. This work is the first spin injection experiment using high-T_C FMS. From the temperature, microwave power, and magnetic field direction dependences of the ISHE voltage as well as the spin pumping experiment on the reference (Ga,Fe)Sb sample, we conclude that the symmetric voltage component obtained in the BiSb/(Ga,Fe)Sb sample has a negligible galvanomagnetic effect. The result presented in this study opens new opportunities for semiconductor-spintronics device applications operating at room temperature.

Methods

Sample growth

The growth of the sample structure is divided into two parts. We first grew a heterostructure composed of (Ga_0.75,Fe_0.25)Sb (50 nm)/AlSb (100 nm)/AlAs (10 nm)/GaAs (100 nm) on a semi-insulating (SI) GaAs (001) substrate with a growth rate of 0.5 μm/h by molecular beam epitaxy (MBE), followed by growth of a 2 nm-thick GaSb cap layer to avoid surface oxidation. The substrate temperature (T_S) was 550 °C for the GaAs and AlAs layers, 470 °C for the AlSb layer, 250 °C for the (Ga,Fe)Sb and GaSb layer. After that, we preserved a half part of the sample as a reference sample and transferred the other half part of the sample to the sputtering system for the BiSb deposition. There, we first etched the GaSb cap layer using Ar-plasma at room temperature. Then, we deposited a 7 nm-thick Bi_0.85Sb_0.15 layer with a rate of 5.8 nm/min on top of the 50 nm-thick (Ga,Fe)Sb layer by co-sputtering Bi and Sb targets with Ar-plasma at room temperature. During the MBE growth, the crystallinity and surface morphology of the samples were monitored in situ by reflection high-energy electron diffraction (RHEED) along the [$\overline{\text{1}}10$] azimuth with respect to the GaAs (001) substrate.

Characterizations

The MCD measurements were performed using a J700 system (built by JASCO Corporation) equipped with an electromagnet and a cryostat. AHE measurements were performed on samples etched into 50 × 200 μm Hall bars using photolithography and ion milling.

Spin pumping measurement

In spin pumping experiments, we used a JEOL electron spin resonance (ESR) spectrometer whose cavity resonates in the transverse electric (TE₀₁₁) mode with a microwave frequency f of 9.14 GHz (X-band). We cut the samples into a 3 × 1 mm² piece with edges along the $[110]$ (3 mm) and $[1\overline{\text{1}}0]$ (1 mm) axes. For electrical measurements, we have connected the two gold wires to the indium contacts at both edges of the sample with a distance of l = 2 mm. The sample was placed on the center of a quartz rod and inserted in the center of the microwave cavity. For the measurements, a static magnetic field μ₀H is applied along the [1$\overline{\text{1}}$0] axis in the film plane (except for the measurements with varying θ_H), which corresponds to the easy magnetization axis of (Ga,Fe)Sb. A microwave magnetic field μ₀h is applied along the [110] axis. Also, an ac modulation field μ₀H_ac (1 mT, 100 kHz) parallel to H is superimposed to obtain the FMR spectrum in its derivative form. The voltage between the indium contacts is detected by a nano-voltmeter (see S.I. Section 4).

Author contributions

S.G., L.D.A., and P.N.H. planned the research. S.G. grew the (Ga,Fe)Sb film using MBE, characterized the samples, fabricated the Hall bar, and performed a Spin pumping experiment. N.H.D.K., and Y.O. help in BiSb growth and analyzing BiSb topological behavior. S.G., L.D.A., P.N.H., and M.T. analyzed the data. L.D.A. and P.N.H. also help in conceptualization and funding acquisition. M.T. performed project administration and managed the research including funding acquisition. S.G. and P.N.H. wrote the manuscript with comments from L.D.A. and M.T.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Competing interests

The authors declare no competing interests.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-023-29169-9.